Question

A car drives 215km east and then 45km north. What is the magnitude of the cars displacement? Round you answer to nearest whole number.

Answer 1

Answer:
`219.65\ \text{km}`

Step-by-step explanation:

Given

Car drives 215 km east and then 45 km North

Displacement is East direction is

`\Rightarrow \vec{r_1}=215\hat{i}`

Now, the displacement from that to 45 km North is given by

`\Rightarrow \vec{r_(21)}=45\hat{j}`

Net displacement is
`\vec{r_2}`

`\Rightarrow \vec{r_2}=\vec{r_1}+\vec{r_(21)}\\\Rightarrow \vec{r_2}=215\hat{i}+45\hat{j}`

Magnitude of the displacement is

`\Rightarrow \left | r_(2) \right |=√(\left ( 215 \right )^2+\left ( 45 \right )^2)\\\Rightarrow \left | r_(2) \right |=√(48250)\\\Rightarrow \left | r_(2) \right |=219.65\ \text{km}`